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Wound roll generated unstable vibration

Jorkama, M.
von Hertzen, R.
Nip contact between the wound roll and the winding drum, rider roll or some other nip roller may cause that the wound roll is deformed into a convex polygon. This deformation process is accompanied with a very strong vibration. The conditions under which this phenomenon occurs depend much on the web properties. For example, in the paper industry some bulky grades with a high layer-to-layer COF are known to be prone to this unstable vibration.
In this paper a simple wind up model, capable of capturing quite comprehensively this phenomenon, is developed. The polygonal pattern formation is modeled as a viscoelastic surface deformation. This results in linear delay differential equations. In order to analyze the stability, the Laplace transformation is performed for the system equations. The inspection of the root locus shows several zones of instability during the winding cycle. In an example, it is shown how the model can be utilized to explain some well-known winder vibration phenomena.
The paper is concluded by stating general beneficial trends for the wind up design and by explaining how to determine the susceptibility of certain webs to unstable vibration by simple laboratory measurements.